Abstract

This paper is devoted to the definition, analysis and implementation of a new type of subdivision schemes adapted to data (through a stochastic approach) and to a partition of their support. Its construction combines position-dependent multi-scale approximation (Baccou and Liandrat, 2005 [7]) and Kriging theory (Cressie, 1993 [12]). After a full convergence analysis that requires to extend classical results to this new framework, it is applied to data prediction for uni- and bi-variate problems and compared to the Lagrange interpolatory subdivision.